Completing the Square for Conic Sections The Aim

The Aim of Completing the Square … is to write a quadratic function as

Perfect Square Trinomials l x 2 + 6 x + 9 l x 2

The Perfect Square Connection For a perfect square, the following relationships will always be

The Perfect Square Connection l l In the following perfect square trinomial, the constant

Perfect Square Trinomials Create perfect square trinomials. l x 2 + 20 x +

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities

Completing the Square-Example #2 Solve the following equation by completing the square: Step 1:

Slides: 13

Download presentation

Completing the Square for Conic Sections

The Aim of Completing the Square … is to write a quadratic function as a perfect square. Here are some examples of perfect squares! x 2 + 6 x + 9 l x 2 - 10 x + 25 l x 2 + 12 x + 36 l Try to factor these (they’re easy).

Perfect Square Trinomials l x 2 + 6 x + 9 l x 2 - 10 x + 25 l x 2 + 12 x + 36 =(x+3)2 =(x-5)2 =(x+6)2 Can you see a numerical connection between … 6 and 9 using 3 -10 and 25 using -5 12 and 36 using 6

The Perfect Square Connection For a perfect square, the following relationships will always be true … x 2 + 6 x + 9 Half of these values squared x 2 - 10 x + 25 … are these values

The Perfect Square Connection l l In the following perfect square trinomial, the constant term is missing. Can you predict what it might be? X 2 + 14 x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X 2 + 14 x + 49

Perfect Square Trinomials Create perfect square trinomials. l x 2 + 20 x + ___ l x 2 - 4 x + ___ l x 2 + 5 x + ___ l 100 4 25/4

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move the constant term (i. e. the number) to right side of the equation

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. For chapter 10 material, we can stop here. But solving is a simple process from here …

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move the constant to the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. Use calculator to do this!